# Full text of "Analytical Mechanics"

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```MOTION OF A PARTICLE
particle is continually changing, that is, the particle is b< accelerated. Therefore kinetic reaction manifests itself acts in a direction opposed to that of the acceleration, 1 is, away from the point 0. Hence the pull of the str But the pull which comes into play is just enough to 0" come the kinetic reaction, therefore the particle neil approaches to, nor recedes from, the point 0.
Suppose we project the particle with different velocil observe the corresponding readings of the spring bala]
v2
and compute the accelerations from — —, the expression
p
the normal acceleration, p. 94. Let Fi, F2, F3, etc., dei the readings of the balance and /i, /2, /3, etc., denote accelerations; then we shall find that the relations befrft the accelerations and the readings of the balance are gi by equations (I).
On the other hand if we fasten particles of different ma to the string and give them equal accelerations, we s find that equations (II) hold true. Therefore we concl that whether the acceleration be due to changes in the n nitude of the velocity, or in the direction, or in both, kinetic reaction equals the product of the mass by acceleration and is opposed to the latter.
The kinetic reaction of the last experiment may be di: entiated from that of the experiments of sections 92 an< by emphasizing the fact that the former comes into ] when there is a normal acceleration, while the latter m fests itself whenever there is acceleration along the tang The resultant or total kinetic reaction is the vector sui the two.
The results of the last few sections may be summed u the following manner :
(a) The tangential kinetic reaction has a magnitude m'v has a direction opposite to that of the tangential acceleratic
Tangential kinetic reaction = — mvr.         (```